Error estimates for approximating non-hyperbolic heteroclinic orbits of maps

Beyn W-J, Hüls T (2004)
Numerische Mathematik 99(2): 289-323.

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Zeitschriftenaufsatz | Veröffentlicht | Englisch
Abstract / Bemerkung
In this paper we consider heteroclinic orbits in discrete time dynamical systems that connect a hyperbolic fixed point to a non-hyperbolic fixed point with a one-dimensional center direction. A numerical method for approximating the heteroclinic orbit by a finite orbit sequence is introduced and a detailed error analysis is presented. The loss of hyperbolicity requires special tools for proving the error estimate - the polynomial dichotomy of linear difference equations and a ( partial) normal form transformation near the non-hyperbolic fixed point. This situation appears, for example, when one fixed point undergoes a flip bifurcation. For this case, the approximation method and the validity of the error estimate is illustrated by an example.
Erscheinungsjahr
Zeitschriftentitel
Numerische Mathematik
Band
99
Ausgabe
2
Seite(n)
289-323
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Beyn W-J, Hüls T. Error estimates for approximating non-hyperbolic heteroclinic orbits of maps. Numerische Mathematik. 2004;99(2):289-323.
Beyn, W. - J., & Hüls, T. (2004). Error estimates for approximating non-hyperbolic heteroclinic orbits of maps. Numerische Mathematik, 99(2), 289-323. doi:10.1007/s00211-004-0563-4
Beyn, W. - J., and Hüls, T. (2004). Error estimates for approximating non-hyperbolic heteroclinic orbits of maps. Numerische Mathematik 99, 289-323.
Beyn, W.-J., & Hüls, T., 2004. Error estimates for approximating non-hyperbolic heteroclinic orbits of maps. Numerische Mathematik, 99(2), p 289-323.
W.-J. Beyn and T. Hüls, “Error estimates for approximating non-hyperbolic heteroclinic orbits of maps”, Numerische Mathematik, vol. 99, 2004, pp. 289-323.
Beyn, W.-J., Hüls, T.: Error estimates for approximating non-hyperbolic heteroclinic orbits of maps. Numerische Mathematik. 99, 289-323 (2004).
Beyn, Wolf-Jürgen, and Hüls, Thorsten. “Error estimates for approximating non-hyperbolic heteroclinic orbits of maps”. Numerische Mathematik 99.2 (2004): 289-323.